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Proceedings of the American Mathematical Society

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Spectrally determined growth is generic

Author: Michael Renardy
Journal: Proc. Amer. Math. Soc. 124 (1996), 2451-2453
MSC (1991): Primary 47D06
MathSciNet review: 1328372
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Abstract: Let $A$ be the infinitesimal generator of a $C_0$-semigroup of operators in a Hilbert space. We consider the class of operators $A+B$, where $B$ is bounded. It is proved that the spectrum of $A+B$ determines the growth of the associated semigroup for ``most" operators $B$ (in the sense of Baire category).

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Michael Renardy
Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123

Keywords: Linear stability, semigroups of operators
Received by editor(s): January 9, 1995
Received by editor(s) in revised form: February 23, 1995
Additional Notes: This research was supported by the National Science Foundation under Grant DMS–9306635 and by the Office of Naval Research under Grant N00014–92–J–1664.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society